SAN FRANCISCO , California -LRB- CNN -RRB- -- Opponents of California 's voter-approved ban on same-sex marriages launched a new court challenge Wednesday , led by lawyers who were on opposite sides of the case that settled the 2000 presidential race .

A crowd protests the court ruling upholding Proposition 8 in Los Angeles , California , Tuesday .

Attorneys Ted Olson and David Boies have asked a federal judge to block California from enforcing the ban , known as Proposition 8 .

`` We are two lawyers from opposite ends of the political spectrum who have come together to support one of the most important issues of our time , '' Olson told reporters .

The case `` is not about liberal or conservative , Democrat or Republican . We 're here in part to symbolize that , '' he added .

Wednesday 's lawsuit was filed on behalf of two same-sex couples who have been denied marriage licenses under Proposition 8 . A federal judge in San Francisco has set a July 2 hearing on the matter . Watch the next fight about marriage ''

`` Our Constitution guarantees every American the right to be treated equally under the law , '' Boies said . `` There is no right more fundamental than the right to marry the person you love and to raise a family . '' Watch more on the same-sex marriage battle in California ''

Olson was the lead attorney for George W. Bush in the 2000 Florida recount . Boies , meanwhile , was the top legal strategist for former Vice President Al Gore , that year 's Democratic presidential nominee .

California 's Supreme Court rejected a challenge to the marriage ban Tuesday , but left intact about 18,000 same-sex marriages conducted before voters approved the ban in November . The court rejected arguments that the measure improperly amended the state constitution .

In another echo of past political battles , one of those who argued in favor of Proposition 8 was Kenneth Starr -- the special prosecutor who led the Whitewater investigation that led to the 1998 impeachment of President Bill Clinton .

The lawsuit is backed by the American Foundation for Equal Rights , a newly formed organization based in Los Angeles . See iReporter photos of protests , celebrities ''

But a coalition of groups that fought the ban in California courts -- including the American Civil Liberties Union , the Human Rights Campaign and the Lambda Legal Foundation -- urged supporters Wednesday to turn their energy toward winning in the political arena rather than the courts .

`` Pushing the federal government with multiple lawsuits before we have a critical mass of states recognizing same-sex relationships or suing in states where the courts are n't ready is likely to lead to bad rulings , '' the coalition said . `` Bad rulings will make it much more difficult for us to win marriage , and will certainly make it take much longer . ''

Opponents of the ban are already planning to put a new initiative on California ballots in 2010 to repeal it . But Jim Garlow , senior pastor of Skyline Wesleyan Church in San Diego , said on CNN 's `` Larry King Live '' that polls show same-sex marriage advocates losing ground .

`` Right now , Californians support traditional , natural marriage 49 percent compared to 43 percent for same-sex marriage , '' said Garlow , who supported Proposition 8 . `` That 's a reversal . It has just switched in recent months . As people get more familiar with the reality , the sanctity of marriage , how special marriage is , why a child should have a mom and dad , they shift to the traditional marriage view . ''

The suit filed by Boies and Olson cites heavyweight Supreme Court precedents such as Brown v. Board of Education , the 1954 decision that banned segregation in public schools , and Loving v. Virginia , the 1967 ruling that struck down state laws banning interracial marriage .

It also cited Romer v. Evans , a 1996 decision that killed an amendment to Colorado 's constitution that rolled back gay rights ordinances . That measure , like Proposition 8 , had been approved by voters .

`` We 're going to court because people should n't have to surrender their fundamental rights to a popular plebiscite , '' Olson said . `` People should not have to beg to be treated equally or wait for decades for popular approval to be treated equally . ''

Four states -- Connecticut , Maine , Massachusetts and Iowa -- approve of same-sex marriages .

Vermont 's Legislature passed a law making same-sex marriages legal that will take effect in September .

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Ted Olson and David Boies appealing to federal court to block Prop 8

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Voters approved ban on same-sex marriage in November

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Same-sex marriage is legal in four states , mostly in New England